Problem: Simplify; express your answer in exponential form. Assume $p\neq 0, y\neq 0$. $\dfrac{{(p^{2}y^{3})^{-5}}}{{(p^{3}y^{-5})^{2}}}$
To start, try simplifying the numerator and the denominator independently. In the numerator, we can use the distributive property of exponents. ${(p^{2}y^{3})^{-5} = (p^{2})^{-5}(y^{3})^{-5}}$ On the left, we have ${p^{2}}$ to the exponent ${-5}$ . Now ${2 \times -5 = -10}$ , so ${(p^{2})^{-5} = p^{-10}}$ Apply the ideas above to simplify the equation. $\dfrac{{(p^{2}y^{3})^{-5}}}{{(p^{3}y^{-5})^{2}}} = \dfrac{{p^{-10}y^{-15}}}{{p^{6}y^{-10}}}$ Break up the equation by variable and simplify. $\dfrac{{p^{-10}y^{-15}}}{{p^{6}y^{-10}}} = \dfrac{{p^{-10}}}{{p^{6}}} \cdot \dfrac{{y^{-15}}}{{y^{-10}}} = p^{{-10} - {6}} \cdot y^{{-15} - {(-10)}} = p^{-16}y^{-5}$